Triplet Extension of the MSSMand its Higgs Physics
Germano Nardini
Universitat Bielefeld
SUSY 2013
Based onA. Delgado, G.N., M. Quiros
arXiv:1207.6596 , arXiv:1303.0800
Germano Nardini Triplet Higgs Physics
Outline
Outline
1 IntroductionThe model
2 Higgs PhenomenologySpectrumFeatures of the decoupling limitFeatures at small mA
3 Conclusion
Germano Nardini Triplet Higgs Physics
Introduction
Motivation
No clear discrepancies between data and SM predictions withmh ' 126 GeVIf we do not give up with the (Planck/GUT - EW) hierarchyproblem, SUSY is (one of) the favourite UV optionIn the MinimalSSM mh ' 126 GeV requires “heavy” stopsector ⇒ Little Hierarchy Problem, i.e. some fine-tuningNon-minimalSSM models can alleviate this problem as theycan enhance the tree-level Higgs mass via
D–terms: Extra gauge interactionsF –terms: Extra scalar sector (singlets and/or triplets)
If Γ(h→ γγ) is confirmed by future data. . .
. . . the extra charged fermions in the triplet superfield are(potentially) largely coupled to the Higgs and can make the job
Germano Nardini Triplet Higgs Physics
Introduction The model
The Y=0 Triplet Extension (Espinosa&Quiros’92)
Σ =
(ξ0/√
2 −ξ+2
ξ−1 −ξ0/√
2
), ∆W = λH1·ΣH2+
1
2µΣtrΣ
2+µH1·H2
T parameter bound requires 〈ξ0〉 . 4 GeV which imposes(unless of fine-tuning)
|Aλ|, |µ| , |µΣ| .m2
Σ + λ2v2/2
102 λv
This hierarchy implies decoupling between ξ0 and H1, H2
Mass boost: V (H1, H2) ' VMSSM + λ2|H01H
02 |2
(other tripl. SUSY extens. in E.J.Chun&al,1209.1303; Z.Kang&al,1301.2204)
Germano Nardini Triplet Higgs Physics
Phenomenology Spectrum
The relevant spectrum
Heavy scalar triplet [ & 1 TeV ]
Minimiz. conditions
m23 = m2
A sinβ cosβ , m2Z =
m22−m2
1cos 2β −m
2A + λ2
2 v2
CP-odd/charged Higgses [ no preferences ]
m2A = m2
1 +m22 + 2|µ|2 + λ2
2 v2 , m2
H± = m2A +m2
W+λ2
2 v2
Charginos [ O(100 GeV) if diphoton excess ]
(W−, H−
1 , ξ−1
)M±
ch
W+
H+2
ξ+2
, M±ch =
M2 gv2 0gv1 µ −λv2
0 −λv1 µΣ
Germano Nardini Triplet Higgs Physics
Phenomenology Spectrum
The relevant spectrum
CP-even Higgs masses (basis h2, h1)
M20 =
(m2A cos2 β +m2
Z sin2 β (λ2v2 −m2A −m2
Z) sin 2β/2
(λ2v2 −m2A −m2
Z) sin 2β/2 m2A sin2 β +m2
Z cos2 β
)
After including radiative corrections ∆M2t(ht) and ∆M2
Σ(λ)(also in the min.condts) [mh = 126 GeV](
h2
h1
)=
(cosα sinα− sinα cosα
)(hH
)
Coupling ratios rHXX = gHXX/gSMhXX (H = h,H)
r0hV V r0
HV V r0htt r0
Htt r0hdd r0
Hdd
sin(β − α) cos(β − α)cosα
sinβ
sinα
sinβ− sinα
cosβ
cosα
cosβ
Germano Nardini Triplet Higgs Physics
Phenomenology Features of the decoupling limit
Decoupling limit mA →∞
If mA� mh . . .
Germano Nardini Triplet Higgs Physics
Phenomenology Features of the decoupling limit
Decoupling limit mA →∞
Tree-level Higgs mass
m2h = m2
Z cos2 2β + λ2v2 sin2 2β/2
Little hierarchy problem pushes towards small tanβ and large λ,but perturbation theory may break down at the scale Λ
106
108
1010
1012
1014
1016
1018
0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
1
2
3
4
5
6
Λ
tanΒ
.
curves:1018, 1016, 1014, . . . , 106
Λ .
Germano Nardini Triplet Higgs Physics
Phenomenology Features of the decoupling limit
Decoupling limit mA →∞Signal strength Rγγ [ = BR(h→ γγ)/BR(h→ γγ)SM]
∂
∂ log vlog detMch(v) = − v2(λ2M2 + g2µΣ) sin 2β
M2µµΣ − 12λ
2v2(λ2M2 + g2µΣ) sin 2β
ATLAS: 1.65± 0.30; CMS: 0.8− 1.1± 0.3Loop-induced process which is sensitive to new chargedparticlesNew triplet charged fermion can enhance Rγγ (. 1.1 via MSSM
charginos; e.g. Casas,Moreno,Rolbiecki,Zaldivar ’13)
As no (large) modifications in the Higgs production exist formA →∞, the diphoton enhancement is (easily implemented from
the QED eff.pot. Ellis&al,79; Shifman&al,79; Carena&al,12)
Rγγ =
∣∣∣∣1 +(
43
∂∂ log v log detMch(v)
)/
(A1(τW ) +
4
3A1/2(τt)
)∣∣∣∣2Germano Nardini Triplet Higgs Physics
Phenomenology Features of the decoupling limit
Decoupling limit mA →∞Signal strength Rγγ [ = BR(h→ γγ)/BR(h→ γγ)SM]
∂
∂ log vlog detMch(v) = − v2(λ2M2 + g2µΣ) sin 2β
M2µµΣ − 12λ
2v2(λ2M2 + g2µΣ) sin 2β
1.15
1.2
1.25
1.3
1.35
1.4
1.45
1.5
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
1
2
3
4
5
6
Λ
tanΒ
1.1
1.15
1.2
1.25
1.3
1.35
1.4
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
1
2
3
4
5
6
Λ
tanΒ
M2 = 250 GeV Xt =4, 0; mQ = 700 GeV M2 = 750 GeVµ = µΣ → mχ±
1∼ 105 GeV
Germano Nardini Triplet Higgs Physics
Phenomenology Features of the decoupling limit
Decoupling limit mA →∞
S and T parameters (due to EWKinos)
αS =s2Wλ2
10π2
m2Wµ2
[1 + 19
24 sin 2β]
+O(g4) , S = 0.04± 0.09
αT = 3λ2
128π2
m2Wµ2 cos2 2β +O(g4) , T = 0.07± 0.08
0.06
0.07
0.08
0.09
0.1
0.11
0.12
0.6 0.8 1.0 1.2 1.4
1
2
3
4
5
6
Λ
tanΒ
0.01 0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.6 0.8 1.0 1.2 1.4
1
2
3
4
5
6
Λ
tanΒ
S T
[M2 = 250 GeV, µ = µΣ → mχ±1∼ 105 GeV]
Germano Nardini Triplet Higgs Physics
Phenomenology Features at small mA
Small mA
And now let us
DECREASE mA
without upsetting the h Higgssignatures
Germano Nardini Triplet Higgs Physics
Phenomenology Features at small mA
Small mA (similar idea in C.Wagner’talk)
CP-even Higgs masses (basis h2, h1)
M20 =
(m2A cos2 β +m2
Z sin2 β (λ2v2 −m2A −m2
Z) sin 2β/2(λ2v2 −m2
A −m2Z) sin 2β/2 m2
A sin2 β +m2Z cos2 β
)(h2
h1
)=
(cosα sinα− sinα cosα
)(hH
)Tree-level h couplings are SM-like if α = β − π/2. With M2
0:
βc = π4 , λc=
√2mhv
More generically with M2, fixing h mass yields (no m4A!):
A(tanβ, λ,mh)m2A +B(tanβ, λ,mh) = 0
SM-LIKE POINT (λc, tanβc) INDEPENDENT OF mA
Germano Nardini Triplet Higgs Physics
Phenomenology Features at small mA
Small mA
tanβ(λ) and sinα(λ) fixing mh = 126 GeV
0.85 0.90 0.95
1
2
3
4
5
6
Λ
tanΒ
0.85 0.90 0.95
-0.6
-0.4
-0.2
0.0
0.2
Λ
sinΑ
Radiative correction ∆M2t(ht) and ∆M2
Σ(λ) included(mQ = 700 GeV, At = 0, mΣ = 5 TeV).Curves: mA =∞, 200, 155, 145,140,135,130 GeV
No attempt to reproduce data with mH = 126 GeV (but worth tocheck!)
Germano Nardini Triplet Higgs Physics
Phenomenology Features at small mA
Small mA
Signal strengths RHXX
RHXX =σ(pp→ H)BR(H → XX)
[σ(pp→ h)BR(h→ XX)]SM
R(ggF )HXX = R(Htt)
HXX =r2Htt r
2HXXD
, R(V BF )HXX = R(VH)
HXX =r2HWW r2
HXXD
D = BR(h→ b b)SM r2Hbb + BR(h→ gg, cc)SM r2
Htt
+ BR(h→ ττ)SM r2Hττ +BR(h→WW,ZZ)SM r2
HWW
No extra inv. width, i.e. mχ0 & mH/2sbottom-gluino may correct rhbb (M3 =1 TeV,mb=700 GeV)
Germano Nardini Triplet Higgs Physics
Phenomenology Features at small mA
Small mA mA = 140GeV, µ = µΣ = 250GeV, mχ± = 104GeV
Signal strengths RhXX from ggF and htt
RHXX =σ(pp→ H)BR(H → XX)
[σ(pp→ h)BR(h→ XX)]SM
0.90 0.95 1.000.0
0.5
1.0
1.5
2.0
2.5
3.0
Λ
RhXX
HggFL
bb,ττ ,WW ,γγ
Germano Nardini Triplet Higgs Physics
Phenomenology Features at small mA
Small mA mA = 140GeV, µ = µΣ = 250GeV, mχ± = 104GeV
Signal strengths RhXX from VBF and Vh
RHXX =σ(pp→ H)BR(H → XX)
[σ(pp→ h)BR(h→ XX)]SM
0.90 0.95 1.00
0.0
0.5
1.0
1.5
2.0
2.5
Λ
RhXX
HVBFL
bb,ττ ,WW ,γγ
Germano Nardini Triplet Higgs Physics
Phenomenology Features at small mA
Small mA mA = 140GeV, µ = µΣ = 250GeV, mχ± = 104GeV
Signal strengths RHXX from ggF and htt
RHXX =σ(pp→ H)BR(H → XX)
[σ(pp→ h)BR(h→ XX)]SM
0.90 0.95 1.000.0
0.2
0.4
0.6
0.8
1.0
Λ
RHXX
HggFL
bb,ττ ,WW ,γγ
Further reduction if mχ0 . mH/2 (mH ∼138 GeV)
Germano Nardini Triplet Higgs Physics
Conclusion
Conclusion
Triplet extension alleviates the fine-tuninig with respect to theMSSM
At very small mA there are 2 region around λ ≈ 0.9 and λ ≈ 1 thatmimic the signal strength of a SM Higgs. The exact values dependon mΣ, mQ and mU .
Some small deviations from a pure SM Higgs (e.g. γγ, bb, ττ) canalso be encompassed without need of modifying other rates
The argument to prove the existence of the SM-like point is quitegeneric and can be extended to other models (e.g. singlet exts.)
The extra Higgs sector may be at the EW scale but hidden
and only tiny deviations in RhXX may be present
Dedicated analyses on H± and A are worthwhile (generalizations ofL.Diaz Cruz and M.Battaglia’s talks)
Germano Nardini Triplet Higgs Physics
Conclusion
Plot of rhdd
0.85 0.90 0.95
-1.0
-0.5
0.0
0.5
1.0
1.5
Λ
rhbb
0
Germano Nardini Triplet Higgs Physics
Conclusion
Plot of rhtt
0.85 0.90 0.95
0.98
1.00
1.02
1.04
1.06
Λ
rhtt
0
Germano Nardini Triplet Higgs Physics
Conclusion
Plot of rhV V
0.85 0.90 0.95
0.90
0.92
0.94
0.96
0.98
1.00
Λ
rhVV
0
Germano Nardini Triplet Higgs Physics
Conclusion
Plot of rhγγ
0.85 0.90 0.95
0.95
1.00
1.05
1.10
1.15
1.20
1.25
Λ
rhΓΓ
Germano Nardini Triplet Higgs Physics
Conclusion
mχ±1
= 104 GeV (solid line), mχ±1
= 150 GeV with µ = µΣ = 300
GeV (dashed line) and mχ±1
= 200 GeV with µ = µΣ = 350 GeV
(dotted line)
0.90 0.92 0.94 0.96 0.98 1.00
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Λc
tanΒc
mSHTeVL
0.90 0.92 0.94 0.96 0.98 1.00 1.021.10
1.15
1.20
1.25
1.30
1.35
1.40
Λc
RhΓΓ
Germano Nardini Triplet Higgs Physics